1. Field of the Invention
The present invention relates to a method for correcting an exposure mask used in a lithography step for forming a circuit pattern of a semiconductor device, and particularly to a reflective exposure mask applicable for so-called extreme ultra violet light. In addition, the present invention relates to the exposure mask and a method for producing the exposure mask.
2. Description of Related Art
In recent years, as semiconductor devices have been miniaturized, the line widths of resist patterns formed by exposing and developing resist as photosensitive material coated on wafers and further the line widths of circuit patterns obtained by etching the resist patterns as etching masks have been required to be miniaturized. In addition to the line widths, pattern pitches and so forth have also been required to be miniaturized. These requirements have been satisfied by decreasing wavelengths of light used to expose the resist. It is known that the relation between a wavelength of light and a resolution of a pattern can be expressed by the following Rayleigh's formula.w=k1×(λ/NA)  (1)
In the formula (1), a reference code w represents the minimum width of a pattern to be formed; NA represents a numerical aperture of the lens of a projection optical system; and λ represents a wavelength of an exposure light. In addition, it is known that a reference code k1 represents a process constant decided by the performance of the resist and the selection of resolution enhancement technology, and depending on the most suitable resist and resolution enhancement technology, the process constant K1 of around k1=0.35 can be achieved. The resolution enhancement technology is a technology in which a ± first order diffraction light of the light transmitted or reflected by a mask and diffracted by a light insulating pattern disposed on the mask is selectively used to obtain a smaller pattern than the wavelength of the light.
The Rayleigh's formula represents that when a lens of NA=0.9 is used, the minimum pattern width applicable for a wavelength of, for example, 157 nm is w=61 nm. In other words, in order to obtain a pattern width smaller than 61 nm, exposure light having a wavelength of shorter than 157 nm or a liquid immersion lens should be used. When the light having a wavelength of 157 nm and a liquid immersion lens having numerical aperture NA=1.2 are used, the minimum pattern width becomes as small as 46 nm. Thus, after the 45 nm generation, it is discussed to use an exposure light having a wavelength band of around 0.6 nm and a center wavelength of 13.5 nm, and this light is called an extreme ultra violet (EUV) (refer to patent Document 1 listed below). When the EUV and an exposing unit having numerical aperture NA=0.25 are used, a line width of w≧32.4 nm could be formed under the condition of k1≧0.6 according to the Rayleigh's formula.
However, when the EUV having a wavelength of 13.5 nm is used, it is necessary to form an exposure mask and an optical system rather than a transparent mask and an optical system by a reflective mask and a reflective optical system, respectively. In other words, since there exist transparent materials such as Calcium Fluoride (CaF2) and silicon dioxide (SiO2), which can transmit up to an ultraviolet light having a wavelength of 157 nm, a mask and the optical system that can transmit the ultra violet light can be produced. However, there exist no materials that have a desired thickness and transmit the EUV having a wavelength of 13.5 nm.
In addition, when a reflective mask is used, the light reflected on the front surface of the mask should be guided to the projection optical system without mutual interference with the light incident to the mask. Thus, the light that is incident to the reflective mask inevitably has an angle of φ against the normal of the front surface of the mask. In other words, when the resist is exposed with the EUV, the light that is incident to the front surface of the exposure mask has an angle against the normal of the front surface of the mask (for example, refer to the patent Document 2 listed below). This angle depends on the numerical aperture NA of the lens of the projection optical system, the magnification m of the mask, and the intensity σ of the light source. Specifically, when a mask having a magnification of 4× is disposed on a wafer, and when an exposing unit having NA=0.3 is used, the light is incident to the mask with an incident angle greater than 4.30° against the normal of the surface of the mask. Likewise, in an exposing unit having NA=0.25, the light is incident to the mask at an incident angle greater than 3.58°.
In the lithography step of the production process of semiconductor devices, after the light is exposed to wafers, desired transfer images (patterns) should be obtained on the wafers. However, due to the influence of the optical proximity effect, even if an exposure mask is produced in accordance with its designed values, a desired transfer image cannot be always obtained. In particular, when pattern widths, pattern pitches, and so forth are decreased, as patterns are miniaturized, the difference between the mask pattern and the shape of the transferred image tends to become larger. Thus, in consideration of the optical proximity effect, an optical proximity effect correction (OPC) of which a mask pattern on an exposure mask used in the lithography step is corrected in the design stage is performed (refer to for example the patent Document 3 listed below).
The OPC for a mask pattern on an exposure mask is performed in the following manner. When a transparent mask is used, the light is vertically incident to the front surface of the mask. Thus, the center position of a pattern of an image transferred on a wafer matches the center position of a mask pattern on a mask. When a transferred image that is different from a desired pattern is obtained on a wafer, the mask pattern is corrected so that the relation of C=ΔL/Mm is satisfied on the mask. In this formula, a reference code C represents the correction amount of the shape of the pattern on the mask; ΔL represents the difference between the size of the image transferred on the wafer and the size of the desired pattern. In addition, a reference code Mm represents an error factor of the mask that is defined as Mm=(ΔW/ΔM), where ΔMm represents the ratio of ΔM by which the size of the mask pattern is changed to ΔW by which the size of the pattern of the transferred image is changed on the wafer.
Patent Document 1: Japanese Patent Application Unexamined Publication No. 2002-365785
Patent Document 2: Japanese Patent Application Unexamined Publication No. 2003-257810
Patent Document 3: Japanese Patent Application Unexamined Publication No. 2002-122977